📐 Parabola Calculator
Calculate parabola properties
Distance from vertex to focus (p ≠ 0)
How to Use This Calculator
Enter Vertex Coordinates
Input the x and y coordinates (h, k) of the parabola's vertex.
Enter Parameter p
Input the parameter p (distance from vertex to focus). p cannot be zero.
Calculate
Press "Calculate Parabola" to find vertex, focus, directrix, and equation.
Formula
Standard form: (x - h)² = 4p(y - k)
Vertex: (h, k), Focus: (h, k + p), Directrix: y = k - p
About Parabola Calculator
The Parabola Calculator finds the vertex, focus, directrix, and equation of a parabola given its vertex coordinates and parameter p.
When to Use This Calculator
- Conic Sections: Analyze parabola properties
- Geometry: Calculate parabola characteristics
- Physics: Model projectile motion and reflections
Frequently Asked Questions
What is a parabola?
A parabola is a U-shaped curve defined as all points equidistant from a focus point and a directrix line. Standard form: (x - h)² = 4p(y - k) for vertical parabolas.
What is parameter p?
Parameter p is the distance from the vertex to the focus. It determines how "wide" or "narrow" the parabola is. Larger |p| means wider parabola.